How to animate a soft object while it is squashed on the floor?
You could use a Lattice modifier to squish the object:

Create a lattice, scale it in Object mode so that it contains your cylinder, subdivide it in the Properties panel &gt; Object Data &gt; Resolution, give it 2 shapekeys. Give your cylinder a Lattice modifier with the lattice as Object. Select the empty, select its second shapekey and deform it Edit mode, the cylinder should deform as well. Back in Object mode, put the shapekey value at 1. Animate the cylinder.